Q21 of 47 Page 1

Define the term ‘decay constant’ of a radioactive sample. The rate of disintegration of a given radioactive nucleus is 10000 disintegrations/s and 5,000 disintegrations/s after 20 hr. and 30 hr. respectively from start. Calculate the half life and initial number of nuclei at t = 0.

Formulas Used:


Radioactive Decay:


The number of nuclei be . Let be the decay constant.



If the initial decay rate is then the decay rate at time is:



Note that


Half life is the time taken for the sample to be halved and is given by:



Decay constant of a radioactive substance is the ratio of the rate of change of the number nuclei at any given time in the sample to the number of nuclei in the sample at that time.


We know that



Substituting the given values we have,




Dividing the equations, we have




Taking natural log on both sides, we have



The half-life is:



Now, let us find




Note that



Now,





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